Refinement of methods, approaches and techniques developed in this thesis

- This research focused on the influence of congestion effects on the dynamic OD estimation problem. In the case study of section 3.4.2 of the thesis, stop-and-go waves were present on the network. This phenomenon is what we call a second-order effect, and cannot be modeled by a first-order kinematic wave model. The analysis showed that these stop-and-go waves hindered the OD estimation process by troubling the interpretation of the flow and speed measurements (i.e. our method tries to relate the oscillations to changes in the OD matrix). This resulted in a less accurate estimated OD matrix. Extending the developed SBODE method such that it can handle second-order effects would be a natural extension. Our idea regarding this extension is the following. Researchers do not share a unanimous vision on the cause of stop-and-go waves. Some researchers look for explanations in the instability of the traffic flow (e.g. Tampère et al., 2005), while others consider lane changing behavior to be the cause (e.g. Ahn & Cassidy, 2007). Either way, stop-and-go patterns are related to operational characteristics of the flow and do not contain useful information on the OD flows. We conclude that it is thus justified to eliminate the effect of oscillatory traffic patterns on the OD estimation process by applying a preprocessing on the data that removes the second order effects from the measurements before applying the SBODE method. The selection or development of such a ‘first order’ data filter is left for further research.

- In chapter 4, the problem of preserving the congestion pattern during the iterations of the OD estimation was raised. Two possible approaches were suggested: adding constraints, or performing a line search with an adapted goal function. In the end, we chose for the latter, more heuristic approach, mainly because of some practical problems that were encountered with the formulation of the constraints. These practical problems related to translating the constraints from a continuous time formulation to a discrete time formulation, and

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formulating additional constraints that prevent the creation of additional congested areas (see appendix B). We do believe that the idea of adding constraints has potential. Further research is however necessary to resolve the encountered problems. Also the approach of the line search with the adapted goal function has not yet been optimized. More in general, further research on the optimization process (which algorithm to use, how to include constraints, heuristic rules that accelerate convergence) would be an interesting research direction. In this thesis, the computation time gained by using the Gauss-Newton method instead of a steepest descent algorithm already proved to be significantly. More advanced methods might further increase this gain. Special attention should here be given to the combination of the solution algorithm and the inclusion of constraints.

- The results from the density-based approach in chapter 3 did not prove to be entirely satisfactory. Partly because of these results, another research direction was followed that eventually led to the SBODE method that utilizes a refined relationship between link flows and OD flows (see chapter 4). A similar study on the relationship between densities and OD flows might provide us as well useful insights that can be combined in a density-based methodology. The major advantage of densities over link flows is that they uniquely determine the state of a link, and that transitions in the traffic regime do not always lead to a non-monotonic relationship. For example, by increasing the OD flow that needs to pass a bottleneck, the densities on the links upstream of this bottleneck will increase, even when congestion spills back on these links. In such case, there might not even exist a problem of local optima, as opposed to the relationship between link flows and OD flows. Of course, this is just one situation, and it is not necessarily representative for the general relationship between densities and OD flows. Further analysis on this relationship can be useful to develop a method that has less difficulty with transitions of the traffic regime.

- Application of the MaC technique for calculating the sensitivity of the link flows to the OD flows resulted in a computational gain of a factor 3 till 5 in the case studies presented in section 5.2.2. As was discussed, this gain was somewhat less than what was expected based on the results of Corthout et al. (2011). It was concluded that this was because of the different structure of the network (more corridor-like), and a larger amount of congestion in the networks of these case studies. With the development of the hierarchical approach, these are exactly the type of networks that will be considered for the SBODE method, in which case MaC will never reach its full potential. Nevertheless, further enhancements of MaC are possible that can result in considerable extra computational gains. An obvious improvement is a more efficient implementation of the MaC code (possibly involving parallel processing). A more interesting one is the following, more algorithmic enhancement. The current algorithm of MaC is path-based: changes to the path flows are being propagated to all links in the affected area. By doing so, there can be a large overlap in the calculation of this propagation. For example, consider two routes A and B that have a large number of links in common. A change of route flow A will cause the same changes on the common links as a change of route flow B. Therefore, it is inefficient to do these calculations twice. It might be more efficient to use a link-based approach. In this approach, changes to link entry-exit flows would be propagated. So for each link, we would know how changes in the inflow (towards a certain outgoing link) would affect the inflow on each of the outgoing links, and how changes in the outflow (coming from a certain incoming link) would affect the outflow on each of the

incoming links. In the end, the sensitivity of the link flows to the route flows would be derived by assembling the above sensitivities. Since, in general, the number of paths on a link is much higher than the number of entry-exit flows, the computational gain would be much higher, since a large number of repeated calculations would be avoided. The feasibility of such an approach needs further investigation.

- In general, the detector configuration (both the positioning and the number of detectors) has an important impact on the accuracy of the estimated OD flows. In the hierarchical approach, this holds true as well. Actually, the detector configuration has an additional impact on the accuracy in the hierarchical approach. A good subdivision of the network in subareas, on which independent OD estimations are performed, is highly dependent on the detector configuration. This can easily be understood: if there is a subarea with hardly any detectors, then performing an OD estimation on this subarea will result in inaccurate estimated OD flows and link flows. Since these link flows are used as constraints for the OD estimation on the rest of the network (see section 5.2.3), these constraints can degrade the accuracy of estimated OD flows in the rest of the network. While section 5.3.2.2 already provided some guidelines on how to subdivide the network, a further analysis is needed on the relationship between the detector configuration and a good subdivision of the network. The findings of such analysis will also have some implications on the research topic of optimal detector positioning for OD estimation.